Mark answered...

The most direct answer to the question is a group of six men who signed their names to a founding document on April 6, 1830. The room was filled with believers, but six signed to fulfill New York state law. Preeminent among them was Joseph Smith, Jr. who was designated the first elder and apostle by revelation. It is Joseph Smith, Jr. who is most often referred to as the founder of the Church of Jesus Christ of Latter-day Saints.

Joseph, as a young man of eighteen years of age, was visited by an angel, the one mentioned in Revelation 14:6, who told him where an ancient record was buried which contained a history of a group of ancient, American Christians, and which also contained the fullness of the gospel of Jesus Christ. This record was translated by the gift and power of God by the young man with the aid of others as scribes and witnesses of the translation.

During translation they learned of the need of further organization, and this tiny group sought out God who sent additional angelic messengers which conferred authority from God to organize His Church again upon the earth, as it was in Biblical times. This group and those who believed their stories of miraculous events met in a farmhouse on April 6, 1830 in upstate New York to create an officially recognized organization that could hold the copyrights to the record that was translated as the Book of Mormon as well as other rights granted to religious societies.

It is called the Mormon church because of the book revealed from heaven, which is unique from all other Christian churches.